With those words late in a major speech on Tuesday, Prime Minister Theresa May charted Britain’s course toward a clean break with the European Union and expressed her fondest hope: that the time for “division and discord” is over.

Her much-anticipated speech outlined what promised to be a hugely complex, drawn-out negotiation, and it defined the broad objectives, but not the details, of British withdrawal. “The United Kingdom is leaving the European Union, and my job is to get the right deal for Britain as we do,” she said.

With the address, Mrs. May began the jockeying that will lead to a break after more than four decades of tight integration, and define Britain’s relations with its neighbors for decades to come.

She confirmed that Britain is determined to regain control of migration from the European Union and rejected the supremacy of the European Court of Justice. That stance is anathema to the European Union, which has made the free movement of people — as well as goods, capital and services — a bedrock principle and which relies on the court to arbitrate.

“Let me be clear,” Mrs. May said, acknowledging the differences. “What I am proposing cannot mean remaining in the single market.”

She said that she hoped to complete a final deal with the European Union by March 2019 and that it would be voted on by both houses of Parliament. She was not clear about what would happen if Parliament rejected the deal, though some speculated that a rejection would result in the sort of chaotic, “cliff edge” breakup that she and Britain’s bankers and business leaders hoped to avoid.

Mrs. May struck a diplomatic note, including an appeal for a new partnership with Continental Europe, but not at all costs.

“We seek a new and equal partnership — between an independent, self-governing, global Britain and our friends and allies in the E.U.,” Mrs. May said. “Not partial membership of the European Union, associate membership of the European Union, or anything that leaves us half in, half out.”

And she appealed to Britons, especially to those in Scotland, Wales and Northern Ireland, to unite behind the government and stop refighting the referendum that backed leaving the bloc, which she had opposed.

The reaction among her opponents in the “remain” camp was predictably harsh and seemed to herald a long and bruising process.

“Theresa May has confirmed Britain is heading for a hard Brexit,” said Tim Farron, the leader of the centrist Liberal Democrats. “She claimed people voted to leave the single market. They didn’t. She has made the choice to do massive damage to the British economy.”

The Labour leader, Jeremy Corbyn, accused the Tories of turning Britain into “a bargain-basement tax haven,” with their recent threat to slash corporate taxes if a good deal cannot be reached with the European Union.

The speech, which provided some degree of substance, gained a warmer reception in the markets, with the pound seeming to stabilize after several jittery days. It rose as much as 1 percent against the dollar during her speech, while stocks on the London exchange fell.

Carolyn Fairbairn, director general of the Confederation of British Industry, a business lobbying group, welcomed the greater clarity provided by Mrs. May but worried that “ruling out membership of the single market has reduced options for maintaining a barrier-free trading relationship between the U.K. and the E.U.”

Kallum Pickering, senior Britain economist at Berenberg Bank in London, was more blunt, writing in an analysis that “as we do not expect the E.U. to compromise its principles, the U.K. is set to face significant economic consequences from Brexit.”

Few analysts expect the negotiations to go as smoothly or as quickly as Mrs. May seemed to say in her speech. In recognition of the troubles that may lie ahead, Mark Boleat, the policy chairman for the City of London Corporation, the heart of Britain’s financial services industry, urged Mrs. May to swiftly secure a transition deal that would provide the certainty that businesses crave.

Charles Brasted, a partner at Hogan Lovells, an international law firm, cautioned that the deal Mrs. May wanted was likely to be seen by the European Union as “precisely the cherry picking that they have warned against.” He added: “The objectives are now clear. The path towards them is uncharted.”

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The Tower of London on Sunday. Brexit supporters have argued that leaving the European Union will provide new trading opportunities.CreditPeter Nicholls/Reuters

But he warned that “every one of the aspirations expressed by the U.K. government today will demand exceptional political skill to negotiate and will be complex to implement legally and commercially.”

In Europe, Donald Tusk, the president of the European Council, said on Twitter: “Sad process, surrealistic times but at least more realistic announcement on #Brexit.” Germany’s foreign minister, Frank-Walter Steinmeier, welcomed Mrs. May’s “desire for a positive and constructive partnership, a friendship with a strong E.U.,” which Germany would reciprocate.

Mrs. May’s speech, delivered in the grand surroundings of Lancaster House in London, was the most closely watched statement on European policy since January 2013, when the prime minister at the time, David Cameron, promised to hold a referendum on European Union membership.

The prospect that Britain would remain part of the single market has been fading since Mrs. May said in October that she would demand complete control of migration from the European Union and release from the European Court of Justice.

The extent to which Mrs. May would be willing to compromise to maintain some access to the single market and to the customs union for goods was less clear. Membership in the customs union limits the ability of member countries to strike individual free-trade deals with non-European nations. So she said she wanted a deal that would allow Britain to trade freely with the world, but still have as much tariff-free trade as possible with European Union countries.

Ideally, Britain would like to have its cake and eat it, in the memorable phrase of the foreign secretary, Boris Johnson. In other words, Britain would reject what it disliked about the bloc, like freedom of movement, but keep trade unencumbered as it tried to get the best possible trading deal consistent with its other objectives.

While European nations are expected to be stingy with market access, Mr. Pickering says he believes they will eventually bend.

In the final deal, he wrote, he still expects Britain and the European Union to agree to a deal in which “the U.K. maintains a good level of access to the E.U.’s goods markets and limited access to the less-developed services markets.”

“Crucially, we expect the U.K. to lose its E.U. financial services passport,” Mr. Pickering wrote, referring to a system that allowed banks based in Britain to offer financial services throughout the bloc. “This follows from the U.K. raising some modest barriers to migration from the E.U.”

Many European Union countries have backed taking a hard line against Britain to send a message to other member states that might consider leaving. Anticipating that, Mrs. May said that Britain wanted a successful European Union and a friendly partnership, but that “no deal for Britain is better than a bad deal for Britain.”

Correction:Jan. 19, 2017

An article on Wednesday about a speech by Prime Minister Theresa May of Britain in which she charted the country’s course toward a clean break with the European Union misstated the timing of her call to “get on with it.” It came late in the speech, not early.

Melissa Eddy contributed reporting from Berlin, and James Kanter from Brussels.

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